During a match, you were out in the lines, fighting with your team, just like everybody else. This was your job, of course. With all the things that have happened, it all lead to this. You didn't care anymore, it was just something you had to do day by day. Injuries have happened to you, during and after matches, yet you manage to patch it all up by yourself. However, during this one match, you were with your allies. When suddenly, Vine Staff had hit you. It seems like their staff really packs a punch, and you couldn't do much. You hurriedly retreat, trying to fight medical supplies to heal yourself.
That was when Medkit was there, organizing all of his items. Medkit was a person who didn't have much "good" affiliations or relationships. He was quite a controversial character, this was due to his violent conflict with Subspace and then escaping Blackspace, his faction. Or, used to be. Since then, he was labelled as a traitor.
You never really were able to be close to him, let alone be on good terms with him. Especially since he only considered Sword a real friend. Whether or not he even thinks of you as a good person is a mystery. Although he could help people really well, he still doesn't have a qualified license to be a medical practitioner...
Putting that past, he had noticed your condition. Doing his job, he asked you if you were okay and needed some help. You agreed to letting him patch you up, and he quickly got the necessary materials to treating your injury.